The generalization of the lattice cluster theory (LCT) to include explicit trans-gauche energy differences is applied to study the combined influences of chain stiffness disparities, monomer molecular structures, energetic asymmetries, and nonrandom mixing on the miscibilities of binary polymer blends. The combination of all these relevant physical features within a single theory enables testing various divers ent suggestions concerning the dominant physical factors governing the miscibility of polyolefin blends. Thus, tests are presented of models ascribing the observed miscibility patterns in polyolefin blends solely to entropic factors (stiffness disparities) or solely to enthalpic factors (solubility parameter models). The LCT computations demonstrate the combined importance of both factors, as well as several others arising from monomer molecular structures and compressibility. An important and highly nontrivial ingredient in these tests is the novel computation of tile mean square radius of gyration for structured monomer chains. The LCT also provides partial teats of a model in which thermodynamically equivalent semiflexible linear chains replace real polyolefin chains. In addition, we extend to semiflexible chains and to asymmetric polymerization indices a remarkable correlation between the binary blend critical temperature and a structural parameter that depends on the fractions of tri-and tetrafunctional united atom groups in the component chains (for model blends ir which all van der Waals interactions are equal). Several comparisons with experiment for polyolefin blends serve to explain the molecular origins of observed deviations from solubility parameter models for the phase behavior of blends containing poly(isobutylene), as well as for the observed very weak variation of the critical temperature with molecular weights observed in some experimental blends.